please help asap
photo attached
choices are
A. -8
B. -6
C. 0
D. 22

The function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4 is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

A function is said to be continuous if there are no breaks or jumps in the functions

Conditions for continuity of a function

Now, for the given function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4

We need to determine the interval of continuity, We proceed as follows.

Since f(x) = sin⁻¹x, x ≠ π/4 , we know that the minimum value of x is - 1 and its maximum value is 1.

So, x must lie in the interval (-1, 1) for x ≠ π/4,

Now, when x = π/4 f(x) = sinx. We know that x = π/4 lies in the interval (-1, 1).

But we know that f(x) = sinx at x = π/4. So, there is a removable discontinuity at x = π/4.

So, from the left, f(x) is continuous on the interval [-1, π/4) and  from the right, f(x) is continuous on the interval (π/4, 1]

So, combining both intervals, we have f(x) is continous on the interval [-1, π/4) ∪ (π/4, 1] and since f(x) = sinx at x = π/4, there is a removable discontinuity at x = π/4

So, the function f(x) is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

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Step 1 :

Find the mean of the data :

(2+4+6+8) / 4 = 20/4 = 5

Step 2 :

Find the distance between each data and mean.

Distance between 2 and 5 is 3

Distance between 4 and 5 is 1

Distance between 6 and 5 is 1

Distance between 8 and 5 is 3

Step 3 :

Add all the distances :

3+1+1+3 = 8

Step 4 :

Divide it by the number of data :

8 / 4 = 2

2 is the average absolute deviation.

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Answer:

Step-by-step explanation:

Calculating the exact sea level rise resulting from all the melted ice flowing into Earth's oceans requires precise measurements and data that are subject to numerous variables. However, we can provide a rough estimate based on some general assumptions.

According to the National Snow and Ice Data Center (NSIDC), the total volume of ice on Earth is estimated to be approximately 24 million cubic kilometers (km³). If all of this ice were to melt and flow into the oceans, it would contribute to a rise in sea level.

To convert the volume of ice into a rise in sea level, we need to consider the total surface area of the oceans. The approximate surface area of the Earth's oceans is about 361 million square kilometers (km²).

Using these figures, we can estimate the sea level rise as follows:

Sea Level Rise (km) = Volume of Ice (km³) / Surface Area of Oceans (km²)

Sea Level Rise (km) = 24,000,000 km³ / 361,000,000 km² ≈ 0.066 km ≈ 66 meters ≈ 216.5 feet

Therefore, if all the ice on Earth were to melt and flow into the oceans without changing the ocean basin, it could cause the sea level to rise by approximately 0.066 kilometers (66 meters) or 216.5 feet. However, please note that this is a rough estimate and does not account for factors such as thermal expansion of water or the complex dynamics of ice melting and oceanic response, which can affect sea level rise differently in various regions.

The inverses of the following block matrices i 0 c i , a 0 c d , and 0 i i d (assuming they exist) are correct.

To find the inverse of a block matrix, we need to use the following formula:

[A B]

[C D] ^ -1 = 1 / (AD - BC) * [D -B]

[-C A]

where A, B, C, and D are matrices of appropriate sizes and AD - BC is the determinant of the matrix [A B; C D]. If the determinant is zero, the matrix is singular and has no inverse.

(a) [i 0; c i]

The determinant of this matrix is i * i - 0 * c = -c. Since the determinant is non-zero for any non-zero value of c, the matrix has an inverse. Using the formula, we have:

[ i 0 ]

[ c i ] ^ -1 = 1 / (-c * i - 0 * 0) * [ i 0 ]

[-c i ]

= -1 / c * [ i 0 ]

[-c i ]

= [ -1/c 0 ]

[ 0 -1/c ]

To check this inverse, we need to multiply the matrix by its inverse and see if we get the identity matrix:

[ i 0 ]

[ c i ] * [ -1/c 0 ] = [ 1 0 ]

[ 0 1 ]

and

[ i 0 ]

[ c i ] * [ 0 -1/c ] = [ 0 1 ]

[-1 0 ]

So the inverse is correct.

(b) [a 0; c d]

The determinant of this matrix is ad - 0 * c = ad. Since the determinant is non-zero for any non-zero values of a and d, the matrix has an inverse. Using the formula, we have:

[ a 0 ]

[ c d ] ^ -1 = 1 / (ad - 0 * c) * [ d 0 ]

[ -c a ]

= 1 / ad * [ d 0 ]

[ -c a ]

To check this inverse, we need to multiply the matrix by its inverse and see if we get the identity matrix:

[ a 0 ]

[ c d ] * [ d/ad -c/ad ] = [ 1 0 ]

[ 0 1 ]

and

[ a 0 ]

[ c d ] * [ 0 1/ad ] = [ 0 1 ]

[ 0 0 ]

So the inverse is correct.

(c) [0 i; i d]

The determinant of this matrix is 0 * d - i * i = -1. Since the determinant is non-zero, the matrix has an inverse. Using the formula, we have:

[ 0 i ]

[ i d ] ^ -1 = 1 / (-1) * [ d -i ]

[-i 0 ]

= [ -d -i ]

[ i 0 ]

To check this inverse, we need to multiply the matrix by its inverse and see if we get the identity matrix:

[ 0 i ]

[ i d ] * [ -d -i ] = [ 1 0 ]

[ 0 1 ]

and

[ 0 i ]

[ i d ] * [ i 0 ] = [ 0 1 ]

[-1 0 ]

So the inverse is correct.

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Answer:

57064

Step-by-step explanation:

Answer:

180 and 2.5

Step-by-step explanation:

for the second collum over 3 it would be 180

For the one under 150 it would be 2.5

let me know if you need a better explanation

Answer:

3=45   150=5              

Step-by-step explanation:

Answer: The most important aspect in doing algebra is having a pen/pencil and paper in hand. It'll give you a better understanding of the question being posed.

the counting number just before C5F16 is 3,072.

Answer:

x·y

14/t

15s

4(x+2)

Step-by-step explanation:

an algebraic expression must have at least one variable and at least one operation (+,-,×,÷)

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

605

Step-by-step explanation:

11x55=605

any options?

Step-by-step explanation:

I can't answer without and option

The solution to the inequality expression 4 < 3(1-3x) <7 is -1/9 > x > -4/9

The inequality expression is given as:

4 < 3(1-3x) <7

Divide through by 3

4/3 < (1-3x) < 7/3

Remove the brackets

4/3 < 1-3x < 7/3

Subtract 1 from the inequality expression

4/3 -1 < -3x < 7/3 -1

This gives

1/3 < -3x < 4/3

Divide through by -3

-1/9 > x > -4/9

Hence, the solution to the inequality expression 4 < 3(1-3x) <7 is -1/9 > x > -4/9

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Answer:

$33

Step-by-step explanation:

Let the amount of money Corey has be $x.

Amount of money Bryce have= $(x +16)

Total amount= $50

$x +$(x +16)= $50

2x +16= 50

2x= 50 -16

2x= 34

Divide both sides by 2:

x= 34 ÷2

x= 17

Amount of money Bryce have

= $(17 +16)

= $33

Answer:

Step-by-step explanation:

45

The function f(x) = (x-2)(x+4) is a quadratic function that can be written in standard form as f(x) = x^2 + 2x - 8.

To graph this function, we can start by finding the vertex, which is located at x = -b/2a = -2/2 = -1, and then plotting a few additional points to determine the shape of the parabola.

To find the y-coordinate of the vertex, we plug x = -1 into the equation and get f(-1) = (-1)^2 + 2(-1) - 8 = -7. So the vertex is at (-1, -7).

We can also find the x-intercepts by setting f(x) = 0 and solving for x:

(x-2)(x+4) = 0

x-2 = 0 or x+4 = 0

x = 2 or x = -4

So the x-intercepts are at (2, 0) and (-4, 0).

To find the y-intercept, we set x = 0 and get f(0) = (0-2)(0+4) = -8. So the y-intercept is at (0, -8).

Now we can plot these points and sketch the parabola:

```

|

|

|

| *

|

|

------+------------> x

|

|

|

|

|

|

```

The domain of the function is all real numbers, since there are no restrictions on the values that x can take.

To find the range of the function, we can look at the vertex and see that the lowest point on the parabola is at y = -7. Since the parabola opens upward, the range extends from -7 to infinity:

Range: [-7, ∞)

This Took me a long long time

Answer:

A = (1/4)√(4 + 11 + 14)√(-4 + 11 + 14)√(4 - 11 + 14)√(4 + 11 - 14)

A = (1/4)√29√21√7

= about 16.32 mm²

Answer:

  16.27 mm²  (see comment)

Step-by-step explanation:

You want the area of a triangle with side lengths 11 mm and 14 mm, and the angle between them 12.2°.

The area is given by the formula ...

  A = 1/2ab·sin(C)

  A = 1/2(11 mm)(14 mm)·sin(12.2°) ≈ 16.27 mm²

The area of the triangle is about 16.27 square millimeters.

__

Additional comment

If you use Heron's formula for the area from the three side lengths, you find it is about 16.32 mm². That's the trouble with over-specified geometrical figures. The result you get depends on which of the given values you use. (To get the area accurate to 4 sf, the angle needs to be specified to 4 sf: 12.24°.)

  s = (4 +11 +14)/2 = 14.5

  A = √(s(s -a)(s -b)(s -c))

  A = √(14.5(14.5 -4)(14.5 -11)(14.5 -14)) = √(14.5·10.5·3.5·0.5) = √266.4375

  A ≈ 16.32

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Answer:

512(cm)3

Step-by-step explanation:

Step-by-step explanation:

Answer:

h=4

Step-by-step explanation:

3h-18=10-4h

-18=10-7h

-28=-7h

-h=-7

h=7

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

21

Step-by-step explanation:

so this is the way i learned it

compare side to side so CA is 12 and LM is 9 so its 4/3

CB is 8 LN is 6 so its 4/3

so AB is 8 so MN would have to be 4/3 which would made MN 6 so MNL would be 21

Answer:

21

Step-by-step explanation:

ΔLMN ≅ ΔABC with a scale factor of 0.75

If Line AB is similar to Line MN, then Line MN is 6.

Perimeter of ΔLMN

9+6+6=

15+6=

21

The system of equations has infinite many solutions using matrices

From the question, we have the following parameters that can be used in our computation:

x/3 - y = 2

-x/2 + 3y/2 = -3

When represented as matrices, we have

\(\left[\begin{array}{cc|c}\frac13&-1&2\\-\frac12&\frac32&-3\end{array}\right]\)

Calculate the determinant D of the matrix

So, we have

D = 1/3 * 3/2 + 1 * -1/2

Evaluate

D = 0

Because the determinant of the matrix is 0, it means that the equation has infinite many solutions

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Answer: B

Step-by-step explanation:

We can triple all the coordinates, so:

\(A'=(3 \cdot 3, 3 \cdot 3)=(9, 9)\\B'=(6 \cdot 3, 6 \cdot 6)=(18, 18)\\C'(9 \cdot 3, 3 \cdot 3)=(27, 9)\)

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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Answer:

The rate of return will be: 12%

Step-by-step explanation:

Given

As the building was sold for 550000

Return can be calculated by dividing the market value by the net income using the formula

Return = Net income / Market value

           = 66000 / 550,000

           = 0.12  which is 12%

Therefore, the rate of return will be: 12%

Answer:  length of AB

Step-by-step explanation:

\(\overline{AB}\) represents the line segment from point A to point B

\(\overrightarrow{AB}\) represents ray from point A to infinity through point B

AB represents the length of the line segment from point A to point B.

Step-by-step explanation:

We can simplify the given expression using the rules of absolute values:

l-80-20l – 100 + l-100l

= -(20l + 80) - 100 + 100 (since |x| = -x when x is negative)

= -20l - 80

= -20(l + 4)

Therefore, the simplified expression is -20(l + 4).

Answer:

100

Step-by-step explanation:

\( | - 80 - 20| - 100 + | - 100| \\ = | - 100| - 100 + | - 100| \\ = 100 - 100 + | - 100| \\ = | - 100| \\ = \boxed{100}\)

____________

hope it helps!

Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

We have 98 % confidence that the true mean time a student sleeps per night is between 6.2928 hours and  7.1832 hours.

Mean = (8.6 + 8.3 + 7.6 + 6 + 7.1 + 5.6 + 5.1 + 6)/ 8 =  6.7875

Standard deviation = √Σ(x - mean)²/n

Σ(x - mean)² = (8.6 - 6.7875)^2 + (8.3 - 6.7875)^2 + (7.6 - 6.7875)^2 + (6 - 6.7875)^2 + (7.1 - 6.7875)^2 + (5.6 - 6.7875)^2 + (5.1 - 6.7875)^2 + (6 - 6.7875)^2

Standard deviation  : \(\sqrt{11.82875}/8\)

s = 0.42991

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

sample standard deviation

number of samples

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 8 - 1 = 7

Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99

Looking at the t distribution table,

z = 2.998

Margin of error = 2.998 × 0.42/√8

                        = 0.4452

The lower limit of this confidence interval is

6.738 - 0.4452 = 6.2928

The upper limit of this confidence interval is

6.738 + 0.4452 = 7.1832

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